What is the derivative of 2sin^2(x)-cos^2(x) ?

The derivative of 2sin^2(x)-cos^2(x) is 3sin(2x)

What is the first derivative of 2sin^2(x)-cos^2(x) ?

The first derivative of 2sin^2(x)-cos^2(x) is 3sin(2x)

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derivative of

2 sin^{2} (x) - cos^{2} (x)

3 sin (2 x)

Solution steps

\frac{d}{d x} (2 sin^{2} (x) - cos^{2} (x))

Simplify

2 sin^{2} (x) - cos^{2} (x) : 2 - 3 cos^{2} (x)

= \frac{d}{d x} (2 - 3 cos^{2} (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2) - \frac{d}{d x} (3 cos^{2} (x))

\frac{d}{d x} (2) = 0

\frac{d}{d x} (3 cos^{2} (x)) = - 3 sin (2 x)

= 0 - (- 3 sin (2 x))

Simplify

= 3 sin (2 x)

What is the derivative of 2sin^2(x)-cos^2(x) ?
The derivative of 2sin^2(x)-cos^2(x) is 3sin(2x)
What is the first derivative of 2sin^2(x)-cos^2(x) ?
The first derivative of 2sin^2(x)-cos^2(x) is 3sin(2x)